e-mail:
laurel.langford@uwrf.edu
My office location: 207B NH
My office phone number:
715-425-4360
My Schedule
Syllabus
Useful Links:
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Contact
me: e-mail: laurel.langford@uwrf.edu My office location: 207B NH My office phone number: 715-425-4360 My Schedule |
Grading
policies, etc Syllabus |
Useful Links: |
| Monday |
Wednesday |
Friday |
| Jan 28 Symmetries and
Functions Handouts 📽 What is Abstract Algebra? 📽 Function composition is associative |
Videos and homework in place of class Homework 📽 Invertible functions 📽 Permutations are functions 📽 Permutations can be composed |
Groups and subgroups Practice for permutation composition 📽 Properties of a group |
| Feb 4 Proving properties of
groups First Page of definitions and theorems notes Assignment: figure out the proofs of theorems 2 and 3 (by thinking or by reading pgs 196-197 of the textbook) 📽 The Complex numbers are a group under addition |
Discuss the proofs of 2 and 3 |
Finding subgroups of a group Notes with assignment. Checklist: what to know and do for Monday The table for S4 |
| Feb 11 Discuss the proofs of theorems 4-6 | What to study for test 1 |
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| Feb 18 Test 1 | Notes and HW |
Homework: Do 18 b,c,d, 20 and 21 on the problems sheet Remember what mod numbers are. Watch these two videos: First, second |
| Feb 25 Homework: Do 19a,b on the sheet Watch this Khan academy video on 1-1 and onto. |
Notes from class |
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| Mar 4 Notes on isomorphisms, including "onto" proof. Homework problem A1a on page 223 of the textbook. |
Test 2 | |
| Mar 11 Isomorphism example from class Assigned problem is number 22 here |
Euclid's method for greatest common divisors: Notes (with assignment) Video (if you get stuck) |
Notes from today: List of what we did (incl. homework) Scanned page (explanation from prev, HW) Theorem/Definition page handed out |
| Mar 18 |
Test 3 |
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| Mar
25 |
Spring |
Break |
| April 1 Up to date theorem/definition file HW: Prove theorems 25 c, 27b (present in class) pg. 37 # 3, 4, 5, 8 (turn in) |
Pg. 37 # 3, 4, 5, 8 |
Read and 📽 watch theorem 21 proof Prove Theorem 30, 31 part 1, 33 part 1. Hints |
| April 8 Prove theorems 34-37 (uniquness) |
Additional problems to work on. Turn in write-up of Thm 31 proof (both parts) |
Read and 📽 watch problem 30 solution Study for the test: theorems 25, 27, 30-37 |
| April 15 Notes and Homework |
Test 4 | |
| April 22 Today's handouts: Problems and Theorems HWK for Weds: write up problems 32,33 to hand in. Prove theorems 39-42 to discuss |
Work
(write up to turn in) problems 32-36 (you may have already turned in 32
and 33, in which case you will not do those problems again) Complete worked example for 35 Note for 36, you do not have to prove it is an isomorphism, you just have to write down the function. |
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| April 29 Notes |
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| May 6 Homework probs from book (prev week) pg. 54 # 5, 11, 13 Pg 80 # 5 Pg 99 # 5a |
Notes (with my latest typo fixed) Notes on theorems 56 and 19 Read and 📽 watch theorem 21 proof |
Last Class Day Completely optional notes to read about 58 and 59 Study the problems assigned since the last test, and the proofs of theorems: 29.5, 39-42, 44, 45, 46, 47, 50, 54, 56 |
| Office hours: Monday 12:30-4:30 Tuesday 11-3. |
Final Exam: Tuesday May 14th 3:30-5:30 pm |